U.S. President Barack Obama has asserted his administration remains prepared to order strikes against "high-value" targets within Pakistan, but would pursue extremists in Pakistani territory after consulting with Islamabad.

"If we have a high-value target within our sights," Mr. Obama said, "after consulting with Pakistan, we're going after them," he said appearing on the CBS programme "Face the Nation" to describe the strategy unveiled on Friday to focus American counterterrorism efforts in Afghanistan and Pakistan.

But Mr. Obama stressed that the US would respect Pakistani sovereignty and those attacks would not be with American ground forces, implying that he was referring to continued strikes from the air.

But the United States needs to hold that government "more accountable," Mr. Obama said. "This is going to be hard," he added. "I'm under no illusions."

Mr. Obama said his administration remains determined to weaken or destroy Al Qaeda until it no longer presents a threat to the United States. He added that his administration is prepared to continually adjust its strategy in Pakistan and Afghanistan as necessary.

Meanwhile, two of his senior aides who are intimately involved with pursuing US strategy in the area spoke frankly about the challenges posed by Pakistan.

The American commander in the region, Gen. David H. Petraeus, appeared on CNN's "State of the Union" and explained that "there is no intention for us to be conducting operations in there, certainly on the ground, and there is every intention by the Pakistani military and their other forces to conduct those operations."

"Well, we have had our ups and downs," Gen. Petraeus said when asked whether there was trust between the US and Pakistani governments.

Richard C. Holbrooke, US special representative on Afghanistan and Pakistan, said on CNN that success required overcoming tensions between Washington and Islamabad, and he cited what senior Pakistani officials have labelled "the trust deficit."

"The relationship between Pakistan and the United States is immensely complicated and it isn't quite where it should be," he said.

Asked about the difficulty of working with Pakistan given the history of sensitive information being passed on to the security services and then in some cases on to Al Qaeda and the Taliban, Mr. Holbrooke responded: "Well, of course, you're absolutely, right".

"It's a huge concern for General Petraeus and me." Holbrooke also noted that Leon Panetta made his first overseas trip as CIA director to the Pakistan region. "This is going to be his focus," Mr. Holbrooke added.